This paper studies the synthesis and the stability of the cellular automata with mixed rules(MCA). Although the dynamics of MCA are determined by rule tables, the number of rule tables is enormous and brute-force search is almost impossible. We propose three synthesis methods based on the genetic algorithm (GA) which is related to the stability.First, we analyze the stability of the teacher signal which is a periodic control signal of AC/DC converter. The ﬁtness of GA is the local stability of the teacher signal.Second, there are several isolated spatiotemporal patterns without transient phenomena by using the elementary cellular automata (ECA). We analyze the stability of those patterns by using MCA and GA. The fitness of GA is the global stability of an isolated pattern.Finally, there are only isolated spatiotemporal patterns without transient phenomena by using ECA. We synthesize those patterns and analyze the stability. The ﬁtness of GA is the number of times to enlarge transient states for steady states.